Outcomes:MS3.3Volume and Capacity Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms.WMS3.2 Applying Strategies Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigationsWMS3.3 Communicating Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventionsWMS3.4 Reasoning Gives a valid reason for supporting one possible solution over another

Indicators:

·Demonstrates an understanding of the concept of ‘capacity’ (Communicating)·Comparing the capacity of different containers (Reasoning)·Estimating then measuring capacity using informal units (Applying Strategies)·Estimating then measuring the capacity of rectangular containers by packing with cubic centimetre blocks·Estimating then measuring using 100mL units (Applying Strategies)·Recording results of measurement tasks (Communicating)

Investigation:Jimmy wants to purchase the biggest slushy from the candy store and has three containers to choose from. Jimmy needs to find the container with the biggest capacity. Which container should Jimmy choose?

Key Questions: What does capacity mean? (How much a container can hold)What experiments could Jimmy conduct to solve this mystery?

Steps·Read the problem to students.·Encourage students to make their predictions regarding the container with the greatest capacity.·Discuss possible experiments that could be conducted to test the capacity of the containers/·Suggest possible test strategies if necessary

Activity 2: Testing using different unitsAim: To assess student understanding of skills required when measuring capacity.

Key Questions: How do we know when the container is full? Were the results the same for both tests? If not why?

Steps·Predict how many scoops of water will be needed to fill each container·Students will experiment with the scoops and fill each container. Record results·Repeat process predicting how many blocks will be required to fill each container. Test and record.

Activity 3: Testing using formal unitsAim: To assess student understanding of the concept of formal units of measurement within capacity. To confirm the order of capacities using accurate measurement.Key Questions: (If there were different results for previous tests) Which results match the accurate 100mL test results?

Steps·Instruct students we will be testing the containers through 100mL measurements with a measuring jug.·Ask students how they know when there are 100mL in the jug. Discuss and demonstrate accurate measurements.·Test each container. Record results.

Activity 4: Conclusion, reflection on lesson results.

Significant Questions: Which container should Jimmy choose? Is this what you predicted?

Steps·Discuss with students their results from their testing·Compare with individual predictions·Hand out Thank you letters from Jimmy

Opportunities for Assessment:Notes taken whilst observing students.Check that students can:·Define capacity·Tell when a container is full·Repeat units and total number of units to determine capacity of a container·Use accurate formal units·Communicate understanding by answering questions

Photos of Students Performing Measurement StrategiesCollect students worksheets

Volumes of Regular Shapes

Topic: Volume Class: 4/5 Date: 15 September Lesson: 2 of 3

Outcomes:

MS3.3 Volume and Capacity Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms. WMS3.2 Applying Strategies Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigationsWMS3.3 Communicating Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventionsWMS3.5 Reflecting Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content

Indicators: ·Identifies the difference between capacity and volume (Reflecting)·Measure and calculate volume in cm3 (NSW DET, 2004, p. 13)·Communicates understanding of the way to calculate the volume of rectangular prisms, that is, finding the area of the base and multiplying by the number of layers (Applying Strategies, Communicating)·Constructs different rectangular prisms that have the same volume (Applying Strategies)·Identifies the differences between centimeters squared and centimeters cubed (Reflecting)·Explains that objects with the same volume may have different shapes (Communicating, Reflecting)·Represents the net of a 3D shape using accurate measurements

Activity 1: Calculating the Volume of Rectangular Prisms (Rf, A.S., C)Aim: To identify student understanding of the processes involved in calculating volumeof rectangular prisms. Estimate then calculate the volume of a rectangular prism in cubic centimetres, given the volume of one layer and the number of layers (NSW DET, 2004, p. 81).

Key Questions: Does the volume of the shape change when we rearrange the models?How can you tell that the volume is the same when the shape is rearranged?

Steps (Adapted from Teaching Measurement, NSW DET, 2004, p. 98)·How is volume different from capacity?What units are appropriate for measuring the volume of a small rectangular prism?·Show students a model of a rectangular prism (Volume= 36cm). After a brief glance, students estimate the volume.·Ask students to explain how to calculate the volume of this shape, that is, calculate the area of the base layer and multiply by the number of layers.·Collaboratively calculate the volume.

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·Ask students to suggest other rectangular prisms that would have the same volume. Students record their predictions of dimensions that will create prisms of the same volume. How many different arrangements can each student create? (Different arrangements include: 3x4x3cm, 2x6x3cm, 4x9x1cm, 12x1x3cm, 2x9x2cm).·Students create prisms using their predicted dimensions, testing if the same number of cubic centimetre blocks is required for each. (Photograph models created by each student).

Activity 2: Creating and Interpreting 2D Representations of Rectangular Prisms.Aim: To assist students in moving from concrete models to abstract representations, as found in text books (A.S., C).

Key Questions: Can you tell the volume of a shape by only looking at one or two of the faces? Why/Why not?

Steps (Adapted from Teaching Measurement, NSW DET, 2004, p. 91).·Provide each student with a handful of unifix cubes. Students create a rectangular prism.·Students draw top, front and side views of their prisms on grid paper provided. (Photograph model created for each student)·Students rotate the ‘plans’ for their shape, and their peers attempt to recreate the prism (Continue rotating until each student has created each model).

Key Questions: Are the faces of every block shown? Why or why not?What is the area of the net? Do larger nets make larger volume?

Steps·Students draw the net of the rectangular prism they created in Activity 2.·Students fold nets to compare with block shapes

Activity 4: Conclusion, reflection on lesson results.Aim: To consolidate learning (C, Rf).Learning activities at this level focus on developing an understanding of how attributes are measured, rather than memorisation and application of formulas or rules. (NSW DET, 2004, p. 15).

Key Questions: What key ideas have we learnt about the measurement of volume of 3D objects? Which way of representing the 3D prisms did you prefer? Why?

Steps·Students use a visual representation strategy of choice to represent the stages in calculating the volume of a rectangular prism.Extension:Open ended question about volume of a given shape (individual cubes not drawn) – See worksheet.

Measuring Irregular Volumes Using Displacement

Topic: Volume Class: 4/5 Date: 22 September Lesson: 3 of 3

Outcomes:MS3.3 Volume and Capacity Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms. WMS3.2 Applying Strategies Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigationsWMS3.3 Communicating Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventionsWMS3.4 Reasoning Gives a valid reason for supporting one possible solution over anotherWMS3.5 Reflecting Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content

Indicators: ·Defines displacement (Communicating)·Uses negotiated units to create an accurate device for measuring displacement (Reasoning, Applying Strategies).·Measure and calculate volume in cm3 of objects other than rectangular prisms using displacement ·Recognises that an object that displaces 300 mL of water has a volume of 300 cubic centimetres (Reflecting)·Develops strategies for predicting displacement for collections of irregular objects (Applying Strategies)·Explains that objects with the same volume may have different shapes (Communicating, Reflecting) ·Generalises that there is not a direct relationship between mass and volume (Reasoning, Communicating)

Activity 1: Creating a measurement device.Aim: Revising concepts of volume covered in previous lessons. Ensure students are aware of the need to make quantitative measurements. (Rf, A.S.)

Key Questions: What is displacement? What are appropriate units for measuring displaced volume of a small object? How can we create our own accurate measuring device?

Steps (Adapted from Teaching Measurement, NSW DET, 2004, p. 97)·Ask students to define displacement in their own words.·Students suggest appropriate increments to mark on a measuring container, discuss the appropriateness of using 100mL measurements·Students use a smaller measuring jug to systematically record the water level as set units of water are added to the container.

Activity 2: Introducing displacement as a measure of total volume.Aim: To ensure that students are aware of the relation between mL and cm3. (A.S., C)

Key Questions: How can we use the measuring device to prove that 100 centimetre cubes will displace 100mL of water? What strategies did you use to assist you with your prediction? Was this an effective strategy? If ___ marbles displaces ­­­­­____mL, what is the volume of one marble? * This is an extension question aimed at the gifted nature of the students planned for.

Steps ·Place 100 centimetre cubes into a measuring device that contains 100mL of water.·Demonstrate that the water level rises to the 200mL mark·Discuss why this is so.·Students (privately) predict how many marbles will have a total volume that will displace the same amount of water (100mL) through an individual activity.·Conduct experiment to prove/disprove prediction

Key Questions: What strategies can we use to compare displacement with irregular objects?

Steps·Students mark the water level in their measuring container·Students place a handful of irregular objects (rocks/marbles/small Tupperware) into their measuring containers·Students record the new water level of their container before removing the objects from the container·Students will pass their container to another student who will estimate how many marbles/rocks etc will be required to make the water level rise to the indicated level ·Students reflect on their predictions

Activity 4: Conclusion, reflection on lesson results.Aim: To consolidate learning (C, Rf).To assess student understanding and comprehension of the activities fulfilled throughout the lesson by applying knowledge to a new situation.

Key Questions: What key ideas have we learnt about displacement? For what objects would you use displacement rather than other strategies to calculate volume? What amount of marbles/rocks/Tupperware containers are equivalent in volume?

Steps·Student based discussion around the key concepts of displacement and the calculation of volume·Students discuss what amount of marbles/rocks/Tupperware containers are equivalent in volume? ·Is there a relation of the mass of objects and the volume they displace?